Computations on overconvergence rates related to the Eisenstein family

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Computations on overconvergence rates related to the Eisenstein family. / Advocaat, Bryan.

In: Journal of Number Theory, Vol. 259, 2024, p. 112-130.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Advocaat, B 2024, 'Computations on overconvergence rates related to the Eisenstein family', Journal of Number Theory, vol. 259, pp. 112-130. https://doi.org/10.1016/j.jnt.2023.12.005

APA

Advocaat, B. (2024). Computations on overconvergence rates related to the Eisenstein family. Journal of Number Theory, 259, 112-130. https://doi.org/10.1016/j.jnt.2023.12.005

Vancouver

Advocaat B. Computations on overconvergence rates related to the Eisenstein family. Journal of Number Theory. 2024;259:112-130. https://doi.org/10.1016/j.jnt.2023.12.005

Author

Advocaat, Bryan. / Computations on overconvergence rates related to the Eisenstein family. In: Journal of Number Theory. 2024 ; Vol. 259. pp. 112-130.

Bibtex

@article{abf70b22a9454bdcbb4bc701603262d4,
title = "Computations on overconvergence rates related to the Eisenstein family",
abstract = "We provide for primes p≥5 a method to compute valuations appearing in the “formal” Katz expansion of the family [Formula presented] derived from the family of Eisenstein series Eκ⁎. We will describe two algorithms: the first one to compute the Katz expansion of an overconvergent modular form and the second one, which uses the first algorithm, to compute valuations appearing in the “formal” Katz expansion. Based on data obtained using these algorithms we make a precise conjecture about a constant appearing in the overconvergence rates related to the classical Eisenstein series at level p. The study of these overconvergence rates of the members of this family goes back to a conjecture of Coleman.",
keywords = "Computations, Eisenstein series, Overconvergent modular forms",
author = "Bryan Advocaat",
note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",
year = "2024",
doi = "10.1016/j.jnt.2023.12.005",
language = "English",
volume = "259",
pages = "112--130",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Computations on overconvergence rates related to the Eisenstein family

AU - Advocaat, Bryan

N1 - Publisher Copyright: © 2024 Elsevier Inc.

PY - 2024

Y1 - 2024

N2 - We provide for primes p≥5 a method to compute valuations appearing in the “formal” Katz expansion of the family [Formula presented] derived from the family of Eisenstein series Eκ⁎. We will describe two algorithms: the first one to compute the Katz expansion of an overconvergent modular form and the second one, which uses the first algorithm, to compute valuations appearing in the “formal” Katz expansion. Based on data obtained using these algorithms we make a precise conjecture about a constant appearing in the overconvergence rates related to the classical Eisenstein series at level p. The study of these overconvergence rates of the members of this family goes back to a conjecture of Coleman.

AB - We provide for primes p≥5 a method to compute valuations appearing in the “formal” Katz expansion of the family [Formula presented] derived from the family of Eisenstein series Eκ⁎. We will describe two algorithms: the first one to compute the Katz expansion of an overconvergent modular form and the second one, which uses the first algorithm, to compute valuations appearing in the “formal” Katz expansion. Based on data obtained using these algorithms we make a precise conjecture about a constant appearing in the overconvergence rates related to the classical Eisenstein series at level p. The study of these overconvergence rates of the members of this family goes back to a conjecture of Coleman.

KW - Computations

KW - Eisenstein series

KW - Overconvergent modular forms

U2 - 10.1016/j.jnt.2023.12.005

DO - 10.1016/j.jnt.2023.12.005

M3 - Journal article

AN - SCOPUS:85184866229

VL - 259

SP - 112

EP - 130

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

ID: 382976205